1) how to make this in QwtLinearScaleEngine ?
2) What methods should I reimplemented (divide scale)?
3) Is this the class to use ?
Derive from QwtScaleEngine and implement all pure virtual methods.
4) is it possible to save autoScale() and transformation (I want to change the least)?
Yes, but I don't think that you want to do this. I can imagine a log2 based transformation or something irregular f.e when you want to have a scale with gaps, but your transformation doesn't look special to me.

Uwe